Respuesta :
Answer:
a. P= 0.6364
b. P = 0.3636
c. Q = $21.25
d. P = 0.5
Step-by-step explanation:
given data
value of a stock varies = $13 to $24
solution
P (stock value is more than $17)
P = [tex]\frac{(24-17)}{(24-13)}[/tex]
P = [tex]\frac{7}{11}[/tex]
P = 0.6364
and
P (value of the stock is between $17 and $21)
P = [tex]\frac{(21-17)}{(24-13)}[/tex]
P = [tex]\frac{4}{11}[/tex]
P = 0.3636
and
Let the upper quartile be Q
[tex]\frac{(24 - Q)}{(24 - 13)} = 0.25[/tex]
[tex]\frac{(24 - Q)}{11} = 0.25[/tex]
(24 - Q) = 2.75
so
Q = $21.25
and
P(X > 20 | X > 16)
P = [tex]\frac{(24-20)}{(24-16)}[/tex]
P = [tex]\frac{4}{8}[/tex]
P = 0.5
Using the uniform distribution, it is found that:
a) 0.6364 = 63.64% probability that the value of the stock is more than $17.
b) 0.3636 = 36.36% probability that the value of the stock is between $17 and $21.
c) The upper quartile is of 21.25.
d) 0.5 = 50% probability that the stock is more than $20.
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
In this problem, varies each day from $13 to $24 with a uniform distribution, hence [tex]a = 13, b = 24[/tex]
Item a:
[tex]P(X > 17) = \frac{24 - 17}{24 - 13} = 0.6364[/tex]
0.6364 = 63.64% probability that the value of the stock is more than $17.
Item b:
[tex]P(17 \leq X \leq 21) = \frac{21 - 17}{24 - 13} = 0.3636[/tex]
0.3636 = 36.36% probability that the value of the stock is between $17 and $21.
Item c:
This is the 75th percentile, that is, the value of x for which P(X < x) = 0.75.
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
[tex]0.75 = \frac{x - 13}{24 - 13}[/tex]
[tex]x - 13 = 11(0.75)[/tex]
[tex]x = 21.25[/tex]
The upper quartile is of 21.25.
Item d:
Greater than $16, hence [tex]a = 16[/tex].
[tex]P(X > 20) = \frac{24 - 20}{24 - 16} = 0.5[/tex]
0.5 = 50% probability that the stock is more than $20.
A similar problem is given at https://brainly.com/question/13547683
